AP Statistics: More Extrapolation

After Friday, I didn’t feel like my students had a firm grasp on the definition of extrapolation and its (possible) consequences. In case you forgot:

4.2 Cautions about Correlation and Regression1_4

So, I was messing around on google, looking for some good examples of extrapolation, and I found this perplexing graph:

4.2 Cautions about Correlation and Regression1_8

We started with an explanation of the stock market, the NASDAQ, and the possible implications of each of them. We also discussed what could happen with inaccurate predictions in this context.

So, I decided to cut the graph back to the original data, and have my students extrapolate and predict the NASDAQ at the end of 2003.

4.2 Cautions about Correlation and Regression1_6

My biggest mistake was giving them the data with the graph. Most of my students wanted to use their calculator and come up with the best prediction model using logarithms. I’m not upset that they decided to go there…I just wanted them to give a quick prediction based off of the trend they could see. Eventually, they got here:

IMG_3277

IMG_3276

…and we looked at the predictions of the entire class (in which all of them followed the same basic trends):

4.2 Cautions about Correlation and Regression1_7

Finally, we looked at the actual value:

4.2 Cautions about Correlation and Regression1_10

In this case, they were wrong. By a lot. And we discussed why. I’m must hoping that this helps emphasize what extrapolation is and its implications…

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